Uniform convergence of regularization methods for linear ill-posed problems

AbstractAfter a general discussion about convergence and convergence rates for regularization methods in Banach spaces, we present a general method that can be used to modify regularization methods in L2 in such a way that uniform convergence, which is often preferred in concrete applications to just L2-convergence, is obtained. We prove results about convergence rates in the uniform norm and discuss questions of parameter choice. The theoretical results will be supported by numerical examples, which indicate that although the results are asymptotic in character, they are of some relevance also for actual computations